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Concepts In AlgebraConcepts-In-Algebra

  • Subject: Algebra
  • |
  • Grade(s): 9-12
  • |
  • Duration: Three class periods

Lesson Plan Sections

Objectives


Students will
  • Discover Islamic achievements in mathematics.
  • Understand Al-Khwarizmi's six standard forms of equations.
  • Be able to solve equations in any of the forms.

Materials


Procedures

  1. Have students research the Arabic numeral system and create a poster based on their research using print and Web resources. The following Web sites are a good starting point: Have the students create a bulletin board from their posters.
  2.  
  3. Have students research Islamic contributions to mathematics using print and Web resources. The following Web sites have useful information:
  4. When students have completed their research, ask them to summarize their findings in a one-page report.
  5. Have students choose a partner to share their reports and answer any questions. Then have each student summarize the partner's report for the class, including at least three interesting facts.
  6. Show students how to solve equations in the squares equal to roots form, ax2 = bx, algebraically and geometrically and provide students time for practice.
  7. Show students how to solve equations in the squares equal to numbers form, ax2 = c, algebraically and geometrically and provide students time for practice.
  8. Show students how to solve equations in the roots equal to numbers form, bx = c, algebraically and geometrically and provide students time for practice.
  9. Show students how to solve equations in the squares and roots equal to numbers form, ax2 + bx = c, algebraically and geometrically and provide students time for practice.
  10. Show students how to solve equations in the squares and numbers equal to roots form, ax2 + c = bx, algebraically and geometrically and provide students time for practice.
  11. Show students how to solve equations in the roots and numbers equal to squares form, ax2 = bx + c, algebraically and geometrically and provide students time for practice.

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Evaluation


Use the following three-point rubric to evaluate students' work during this lesson.
  • Three points:  Students were highly engaged in class discussions; produced complete reports, including all of the requested information; clearly demonstrated the ability to solve equations in any of Al-Khwarizmi's six standard forms.
  • Two points:  Students participated in class discussions; produced an adequate report, including most of the requested information; satisfactorily demonstrated the ability to solve equations in any of Al-Khwarizmi's six standard forms.
  • One point:  Students participated minimally in class discussions; created an incomplete report with little or none of the requested information; were not able to solve equations in any of Al-Khwarizmi's six standard forms.

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Vocabulary


algebra
Definition: A generalization of the ideas of arithmetic
Context: Al-Khwarizmi defined the three types of numbers required to perform calculations in algebra: roots, squares, and simple numbers.

completing the square
Definition: Method of solving quadratic equations that turns every quadratic equation into an equivalent equation of the form x2 = c.
Context: Al-Khwarizmi solved quadratic equations by completing the square.

root
Definition: A solution x to an equation
Context: To Al-Khwarizmi, solving an equation meant finding its roots.

simple number
Definition: A number that can be expressed without reference to either a root or a square
Context: One of Al-Khwarizmi's six forms of equations is squares equal to simple numbers, x2 = c, where c is any nonnegative number.

square
Definition: A root multiplied by itself
Context: One of Al-Khwarizmi's six forms of equations is squares equal to roots, ax2 = bx.

quadratic equation
Definition: An equation of the form ax2 + bx + c = 0, where a ? 0
Context: 2x2 + 3x + 5 = 0 is a quadratic equation

quadratic formula
Definition: If ax2 + bx + c = 0, where a ? 0, then
Context: The equation x2 - 4x + 5 = 0 can be solved using the quadratic formula where a = 1, b = -4, and c = 5.

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Academic Standards


National Council of Teachers of Mathematics (NCTM)
The National Council of Teachers of Mathematics provides guidelines for teaching mathematics in grades K-12 to promote mathematical literacy. To view the standards, visit this Web site: http://www.nctm.org/standards/default.aspx?id=58
This lesson plan addresses the following national standards:

  • Understand patterns, relations, and functions; Represent and analyze mathematical situations and structures using algebraic symbols

Mid-continent Research for Education and Learning (McREL)
McREL's Content Knowledge: A Compendium of Standards and Benchmarks for K-12 Education addresses 14 content areas. To view the standards and benchmarks, visithttp://www.mcrel.org/compendium/browse.asp.
This lesson plan addresses the following national standards:

  • Mathematics: Understands and applies basic and advanced properties of functions and algebra
  • Science: Physical Science: Understands the structure and properties of matter; Understands the sources and properties of energy
  • World History: Understands how Islamic civilization contributed to mathematics

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